Eur. Phys. J. Plus (2020) 135: 316
https://doi.org/10.1140/epjp/s13360-020-00292-0

Regular Article

Similarity solutions using Lie group theoretic method for cylindrical shock wave in self-gravitating perfect gas with axial magnetic field: isothermal flow

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh, 211004, India

^* e-mail: gnath@mnnit.ac.in
^** e-mail: gn_chaurasia_univgkp@yahoo.in

Received: 7 November 2019
Accepted: 21 February 2020
Published online: 16 March 2020

Abstract

Propagation of cylindrical shock wave in a self-gravitating perfect gas under the influence of axial magnetic field using Lie group of transformation method is investigated. The flow is considered to be isothermal. Density and magnetic field are assumed to be varying in the undisturbed medium. Two different cases of solutions are brought out by the arbitrary constants appearing in the expressions of infinitesimals of local Lie group of transformations. One is with a power law shock path and the other one is with an exponential law shock path. Numerical solutions are obtained for both the cases of power law and exponential law shock paths. The effects of variation in Alfven-Mach number, gravitational parameter and ambient density variation index for power law shock path and effects of variation in Alfven-Mach number, gravitational parameter and ambient magnetic field variation index on the flow variables in the case of exponential law shock path are studied. Also the effects of increase in value of gravitational parameter and in the strength of ambient magnetic field on the shock strength are investigated. The increase in value of Alfven-Mach number leads to the increase in the density ratio which infers to the decrease in shock strength.